Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces

Details Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces

2005-11-16

arxiv.org/abs/math/0511415v3

Mathematics

Algebraic Geometry

v2: added due credits to the work of Burger, Iozzi and Wienhard. v3: corrected count of connected components for G=SU(p,q) (p

Scientific paper

Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group representations in a reductive Lie group G. In this paper we survey the case in which G is the isometry group of a classical Hermitian symmetric space of non-compact type. Using Morse theory on the moduli spaces of Higgs bundles, we compute the number of connected components of the moduli space of representations with maximal Toledo invariant.

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